Specifically, the coordinate transformations from \(\psi _{j}\)  to azimuthal angles and the Killing time, and from
\(x_{k}\)  to \(\theta _{k}\) , depend non-trivially on the spin parameters and \(\lambda \) .
The coordinate transformation from the \(n + \varepsilon \)  coordinates \(\psi _{j}\)  to \(t\)  and the \(n-1+\varepsilon \) 
angles \(\phi _{k}\)  defines generalized Boyer-Lindquist coordinates
[1]}
\( \begin{split}t &= \sum _{k = 0}^{n - 1 + \varepsilon } \mathcal {A}^{(k)} \psi _{k}, \\\phi _{j} &= a_{j} \sum _{k = 0}^{n - 1 + \varepsilon } \left( \lambda \mathcal {A}_{j}^{(k)} - \mathcal {A}_{j}^{(k-1)}\right) \psi _{k}.\end{split}\) 
